The tv connection will more than likely be with a coax cable, with content from a cable provider or over-the-air antenna, and will connect to the TV's coax input. The mini will connect through either HDMI or VGA input on a digital TV or via a set of rca yellow-video, red and white audio if an analog TV. You switch the TV's input source when wanting to see content from the mini and switch back for tv. Similarly to the set up for a DVD player or VCR.

As ownZero said you should just be able to change TV inputs on the TV remote control to switch from Mac OS X to TV.

Selecting your various input sources on the TV to switch back and forth. You shouldn't have to disconnect / reconnect. You did mention minimizing OS X so I'm guessing your not wanting to be doing both at the same time so this sounds like the easiest option.

If you do want to do a picture in picture type of setup where you can browse the Internet and watch TV at the same time then something like the Elgato eyeTV would definitely be worth looking at , but for what you described I think you should be fine with switching via the remote._________________Phil